Rainbow Method for Factoring Trinomials

The video tutorial introduces the Rainbow Method for factoring trinomials with a lead coefficient greater than one. It explains the process step-by-step, using examples to demonstrate how to apply the method. The tutorial also covers factoring by grouping, showing how to split the middle term and find common factors. The video concludes with a second example to reinforce the learning.

What is the prerequisite knowledge needed before learning the Rainbow Method?

• Ability to solve linear equations

• Knowledge of factoring by grouping

• Understanding of quadratic equations

• Familiarity with polynomial division

In the Rainbow Method, what do you multiply to find the product used for factoring?

• The coefficients of the middle term

• The lead coefficient and the constant term

• The constant term and the middle term

• The lead coefficient and the middle term

What is the purpose of splitting the middle term in the Rainbow Method?

• To create two binomials

• To rewrite it as the sum of two numbers that are factors

• To simplify the equation

• To find the greatest common factor

When factoring by grouping, what should be done after grouping the terms?

• Add the grouped terms

• Divide the grouped terms

• Multiply the grouped terms

• Factor out the greatest common factor from each group

In the first example, what are the two numbers that multiply to -30 and add to 7?

• -3 and 10

• 3 and -10

• 2 and -15

• 5 and -6

What is the result of factoring the expression 6x^2 + 7x - 5 using the Rainbow Method?

• (3x - 1)(2x + 5)

• (2x - 1)(3x + 5)

• (3x + 1)(2x - 5)

• (2x + 1)(3x - 5)

In the second example, what is the product of the first and last terms?

• -30

• 30

• -60

• 60

What are the two numbers that multiply to -60 and add to 17 in the second example?

• 5 and -12

• -3 and 20

• 3 and -20

• 4 and -15

What is the final factored form of 15x^2 + 17x - 4?

• (5x - 1)(3x + 4)

• (3x - 1)(5x + 4)

• (5x + 1)(3x - 4)

• (3x + 1)(5x - 4)

What is the main advantage of using the Rainbow Method?

• It simplifies the equation

• It works for any polynomial

• It is useful when the lead coefficient is not one

• It eliminates the need for factoring by grouping